What is the inverse of the function $$f(x)=e^{2x+1}$$ ?

$$f^{-1}(x)=\frac{\text{ln}(x)-1}{2}$$ .

What is the value of $$\text{log}_b(b)$$ ?

1, because any number raised to the power of 1 is itself.

What is the change of base formula for logarithms?

$$\text{log}_b(a) = \frac{\text{log}_k(a)}{\text{log}_k(b)}$$ for any base k.

What does $$e$$ represent in mathematics?

$$e$$ is the base of the natural logarithm, approximately equal to 2.718.

What is the value of $$\text{log}_b(1)$$ ?

0, because any number raised to the power of 0 is 1.

What is the product rule for logarithms?

$$\text{log}_b(xy) = \text{log}_b(x) + \text{log}_b(y)$$ .

What is the quotient rule for logarithms?

$$\text{log}_bigg(\frac{x}{y}igg) = \text{log}_b(x) - \text{log}_b(y)$$ .

What is the power rule for logarithms?

$$\text{log}_b(x^k) = k \times \text{log}_b(x)$$ .

What is an exponential function?

A function of the form $$f(x) = a \times b^x$$ , where a is a constant, b is the base, and x is the exponent.

Review - Unit 4 Exponential and Logarithmic Functions Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

Back

The base of the logarithm.

2.

FLASHCARD QUESTION

Front

Back

3.

FLASHCARD QUESTION

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5.

4.

FLASHCARD QUESTION

Front

Back

5.

FLASHCARD QUESTION

Front

Which of the following equations represents exponential growth?

Back

6.

FLASHCARD QUESTION

Front

What is the definition of a logarithm?

Back

A logarithm is the exponent to which a base must be raised to produce a given number.

7.

FLASHCARD QUESTION

Front

What is the relationship between exponential and logarithmic functions?

Back

Logarithmic functions are the inverses of exponential functions.

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